Kevin Leahy

Mohamed Abdelnaby, Samuel Honor, Kevin Leahy

Autonomous multi-agent target tracking in GPS-denied and communication-restricted environments (e.g., underwater exploration, subterranean search and rescue, and adversarial domains) forces agents to operate independently and only exchange information during brief reconnection windows. Because transmitting complete observation and trajectory histories is bandwidth-exhaustive, exchanging probabilistic belief maps serves as a highly efficient proxy that preserves the topology of agent knowledge. While minimizing divergence metrics to merge these decentralized beliefs is conceptually sound, traditional approaches often rely on numerical solvers that introduce critical quantization errors and artificial noise floors. In this paper, we formulate the decentralized belief merging problem as Forward and Reverse Kullback-Leibler (KL) divergence optimizations and derive their exact closed-form analytical solutions. By deploying these derivations, we mathematically eliminate optimization artifacts, achieving perfect mathematical fidelity while reducing the computational complexity of the belief merge to $\mathcal{O}(N|S|)$ scalar operations. Furthermore, we propose a novel spatially-aware visit-weighted KL merging strategy that dynamically weighs agent beliefs based on their physical visitation history. Validated across tens of thousands of distributed simulations, extensive sensitivity analysis demonstrates that our proposed method significantly suppresses sensor noise and outperforms standard analytical means in environments characterized by highly degraded sensors and prolonged communication intervals.

Ahmad Ahmad, Mehdi Kermanshah, Kevin Leahy et al.

In this paper, we tackle the challenging problem of delayed rewards in reinforcement learning (RL). While Proximal Policy Optimization (PPO) has emerged as a leading Policy Gradient method, its performance can degrade under delayed rewards. We introduce two key enhancements to PPO: a hybrid policy architecture that combines an offline policy (trained on expert demonstrations) with an online PPO policy, and a reward shaping mechanism using Time Window Temporal Logic (TWTL). The hybrid architecture leverages offline data throughout training while maintaining PPO's theoretical guarantees. Building on the monotonic improvement framework of Trust Region Policy Optimization (TRPO), we prove that our approach ensures improvement over both the offline policy and previous iterations, with a bounded performance gap of $(2ςγα^2)/(1-γ)^2$, where $α$ is the mixing parameter, $γ$ is the discount factor, and $ς$ bounds the expected advantage. Additionally, we prove that our TWTL-based reward shaping preserves the optimal policy of the original problem. TWTL enables formal translation of temporal objectives into immediate feedback signals that guide learning. We demonstrate the effectiveness of our approach through extensive experiments on an inverted pendulum and a lunar lander environments, showing improvements in both learning speed and final performance compared to standard PPO and offline-only approaches.

Victoria M. Dax, Jiachen Li, Kevin Leahy et al.

Graph-structured data is ubiquitous throughout natural and social sciences, and Graph Neural Networks (GNNs) have recently been shown to be effective at solving prediction and inference problems on graph data. In this paper, we propose and demonstrate that GNNs can be applied to solve Combinatorial Optimization (CO) problems. CO concerns optimizing a function over a discrete solution space that is often intractably large. To learn to solve CO problems, we formulate the optimization process as a sequential decision making problem, where the return is related to how close the candidate solution is to optimality. We use a GNN to learn a policy to iteratively build increasingly promising candidate solutions. We present preliminary evidence that GNNs trained through Q-Learning can solve CO problems with performance approaching state-of-the-art heuristic-based solvers, using only a fraction of the parameters and training time.

Anu K. Myne, Kevin J. Leahy, Ryan J. Soklaski

The state of artificial intelligence technology has a rich history that dates back decades and includes two fall-outs before the explosive resurgence of today, which is credited largely to data-driven techniques. While AI technology has and continues to become increasingly mainstream with impact across domains and industries, it's not without several drawbacks, weaknesses, and potential to cause undesired effects. AI techniques are numerous with many approaches and variants, but they can be classified simply based on the degree of knowledge they capture and how much data they require; two broad categories emerge as prominent across AI to date: (1) techniques that are primarily, and often solely, data-driven while leveraging little to no knowledge and (2) techniques that primarily leverage knowledge and depend less on data. Now, a third category is starting to emerge that leverages both data and knowledge, that some refer to as "informed AI." This third category can be a game changer within the national security domain where there is ample scientific and domain-specific knowledge that stands ready to be leveraged, and where purely data-driven AI can lead to serious unwanted consequences. This report shares findings from a thorough exploration of AI approaches that exploit data as well as principled and/or practical knowledge, which we refer to as "knowledge-integrated informed AI." Specifically, we review illuminating examples of knowledge integrated in deep learning and reinforcement learning pipelines, taking note of the performance gains they provide. We also discuss an apparent trade space across variants of knowledge-integrated informed AI, along with observed and prominent issues that suggest worthwhile future research directions. Most importantly, this report suggests how the advantages of knowledge-integrated informed AI stand to benefit the national security domain.

Kevin Leahy, Austin Jones, Cristian-Ioan Vasile

In this work, we focus on decomposing large multi-agent path planning problems with global temporal logic goals (common to all agents) into smaller sub-problems that can be solved and executed independently. Crucially, the sub-problems' solutions must jointly satisfy the common global mission specification. The agents' missions are given as Capability Temporal Logic (CaTL) formulas, a fragment of signal temporal logic, that can express properties over tasks involving multiple agent capabilities (sensors, e.g., camera, IR, and effectors, e.g., wheeled, flying, manipulators) under strict timing constraints. The approach we take is to decompose both the temporal logic specification and the team of agents. We jointly reason about the assignment of agents to subteams and the decomposition of formulas using a satisfiability modulo theories (SMT) approach. The output of the SMT is then distributed to subteams and leads to a significant speed up in planning time. We include computational results to evaluate the efficiency of our solution, as well as the trade-offs introduced by the conservative nature of the SMT encoding.

Austin Jones, Kevin Leahy, Matthew Hale

In this paper, we develop a privacy implementation for symbolic control systems. Such systems generate sequences of non-numerical data, and these sequences can be represented by words or strings over a finite alphabet. This work uses the framework of differential privacy, which is a statistical notion of privacy that makes it unlikely that privatized data will reveal anything meaningful about underlying sensitive data. To bring differential privacy to symbolic control systems, we develop an exponential mechanism that approximates a sensitive word using a randomly chosen word that is likely to be near it. The notion of "near" is given by the Levenshtein distance, which counts the number of operations required to change one string into another. We then develop a Levenshtein automaton implementation of our exponential mechanism that efficiently generates privatized output words. This automaton has letters as its states, and this work develops transition probabilities among these states that give overall output words obeying the distribution required by the exponential mechanism. Numerical results are provided to demonstrate this technique for both strings of English words and runs of a deterministic transition system, demonstrating in both cases that privacy can be provided in this setting while maintaining a reasonable degree of accuracy.

Kasra Yazdani, Austin Jones, Kevin Leahy et al.

As multi-agent systems proliferate and share more user data, new approaches are needed to protect sensitive data while still enabling system operation. To address this need, this paper presents a private multi-agent LQ control framework. Agents' state trajectories can be sensitive and we therefore protect them using differential privacy. We quantify the impact of privacy along three dimensions: the amount of information shared under privacy, the control-theoretic cost of privacy, and the tradeoffs between privacy and performance. These analyses are done in conventional control-theoretic terms, which we use to develop guidelines for calibrating privacy as a function of system parameters. Numerical results indicate that system performance remains within desirable ranges, even under strict privacy requirements.